While grading her students' most recent quiz on equation solving, Mrs. Jones calculated that approximately forty percent of her students answered question number 14 with multiple choice option B, while the other sixty percent answered A or C.
Question #14 from Mrs. Jones's students' most recent quiz:
14) Solve the single variable equation for
n
.
3
(
−
n
+
4
)
+
5
n
=
2
n
n
=
3
no solution
infinitely many solutions
Part 1: Use inverse operations and rules of equation solving to determine the correct answer to Mrs. Jones's quiz question number 14. Include all of your work in your final answer.
Part 2: Use complete sentences to compare the similarities and differences of each of the multiple choice answer options A-C. In your answer, rationalize why a student would choose each of the options as the correct answer.
Part 1:
To solve the equation,
3(-n + 4) + 5n = 2n
First, distribute the 3 to the terms inside the parentheses:
-3n + 12 + 5n = 2n
Now, combine the like terms on the left side of the equation:
2n + 12 = 2n
Now, we'll try to isolate n by subtracting 2n from both sides:
2n - 2n + 12 = 2n - 2n
Which simplifies to:
12 = 0
This statement is false, so the equation has no solution. The correct answer is option B.
Part 2:
Comparing the multiple choice answer options A-C:
Option A: n = 3
This answer would be chosen by a student who might have made a mistake in the process of solving the equation, possibly by not properly combining like terms or not distributing the 3 correctly.
Option B: No solution
This is the correct answer, as shown in our work in Part 1. The equation results in a false statement, meaning no value of n could make it true.
Option C: Infinitely many solutions
This answer would be chosen by a student who might have made a mistake in the process and ended up with a true statement like 0 = 0, which would mean there are infinitely many solutions as any value of n would make the equation true. In this particular case, there's no simple mistake that leads to this answer choice.